In this research, we conducted extensive simulation studies to compare various regression methods to obtain regression parameters in the presence of high multicollinearity. One measure of the degree of collinearity is the variance inflaction factor (VIF). A VIF value greater than 10 is an indication of high colliearity. Based on the simulation, we found that, in the presence of moderate to higher colliearity, the ridge regression and LASSO are less sensitive to multicollinearity and yield estimates with smaller root mean square error (RMSE). On the other hand, the usual dimension reduction method, i.e., PCR and PLSR, yielded biased estimates. This simulation suggested that LASSO and ridge regression are two appropriate methods for analyzing brain imaging data with high collinearity.